Elliptic curve isogeny class with Cremona label 446160ck (LMFDB label 446160.ck)

• Label: 446160ck
• Number of curves: $4$
• Conductor: $446160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 446160ck have rank \(1\).

Complex multiplication

The elliptic curves in class 446160ck do not have complex multiplication.

Modular form 446160.2.a.ck

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 446160ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
446160.ck4	446160ck1	\([0, -1, 0, 2386087960, 831381003488112]\)	\(75991146714893572533071/15147028085515223040000\)	\(-299465979848366687053739458560000\)	\([2]\)	\(1625702400\)	\(4.9109\)	\(\Gamma_0(N)\)-optimal^*
446160.ck3	446160ck2	\([0, -1, 0, -119445336040, 15431074064812912]\)	\(9532597152396244075685450929/313550122650789880627200\)	\(6199077085028091711161526701260800\)	\([2]\)	\(3251404800\)	\(5.2574\)	\(\Gamma_0(N)\)-optimal^*
446160.ck2	446160ck3	\([0, -1, 0, -599807258600, 178829706213510000]\)	\(-1207087636168285491836819264689/236446260657750000000000\)	\(-4674686725976775146496000000000000\)	\([2]\)	\(4877107200\)	\(5.4602\)	\(\Gamma_0(N)\)-optimal^*
446160.ck1	446160ck4	\([0, -1, 0, -9597367258600, 11443961975461510000]\)	\(4944928228995290413834018379264689/189679641808585500000\)	\(3750082159404878924470272000000\)	\([2]\)	\(9754214400\)	\(5.8067\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 446160ck1.